Heat transfer between tracer and pipe

ABSTRACT

A heat transfer element includes curved mounting surfaces configured to mate with an outer surface of a pipe for attachment thereto; and a channel configured to receive a tracer therein. The heat transfer element is configured to effect conductive heat transfer from the tracer to the pipe, or to process flowing through the pipe, when attached with heat transfer cement (HTC) to both the pipe and the tracer. A system includes a pipe and a tracer; HTC; and a heat transfer element having curved mounting surfaces configured to mate with an outer surface of the pipe and attached thereto via the HTC, and a channel in which the tracer is received and secured via HTC. The heat transfer element is configured to effect conductive heat transfer from the tracer to the pipe, or to process flowing through the pipe, when attached with HTC to both the pipe and the tracer.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a U.S. continuation patent application of,and claims priority under 35 U.S.C. §120 to, U.S. nonprovisional patentapplication 13/154,142 filed Jun. 6, 2011, which '142 applicationpublished as U.S. patent application publication 2011/0297360, whichpatent application and patent application publication are herebyincorporated herein by reference, and which '142 application is a U.S.continuation patent application of, and claims priority under 35 U.S.C.§120 to, international patent application no. PCT/US2009/066904, filedDec. 6, 2009, which international patent application published as WO2010/065946, which international patent application and internationalpatent application publication are hereby incorporated herein byreference, and which international patent application is, for purposesof the U.S., a U.S. nonprovisional patent application of, and claimspriority under 35 U.S.C. §119(e) to, U.S. provisional patent applicationSer. No. 2008, filed Dec. 6, 2008, and U.S. provisional patentapplication Ser. No. 61/167,023, filed Apr. 6, 2009. Each of theseprovisional patent applications is also hereby incorporated herein byreference.

COPYRIGHT STATEMENT

All of the material in this patent document is subject to copyrightprotection under the copyright laws of the United States and othercountries. The copyright owner has no objection to the facsimilereproduction by anyone of the patent document or the patent disclosure,as it appears in official governmental records but, otherwise, all othercopyright rights whatsoever are reserved.

BACKGROUND OF THE INVENTION

The present invention generally relates to heat transfer from a tracingsystem to a pipe system, and more specifically to methods, systems, andapparatus for conductive heat transfer between a tracer and a pipe.

Insulation

It will be appreciated that pipes, and pipe systems, are widely used forinnumerable disparate functions, such as, for example, transportingwater or other fluids. It is often desirable to maintain a fluidtransported via a pipe system, such as water, above an ambienttemperature of an environment in which the pipe is located. In thisevent, insulation is commonly used to try to minimize heat loss.

As an example, consider turbulent hot water flowing at two hundreddegrees Fahrenheit (200° F.) through a four inch (4″) schedule 40 carbonsteel pipe disposed in an environment where the temperature of thesurrounding atmosphere is twenty degrees Fahrenheit (20° F.) with highwinds (It should be noted, and will be appreciated, that this example,as well as several other numerical examples utilized herein, representapproximations of beliefs that it is believed are helpful in conveying ageneralized understanding to a skilled artisan). To attempt to minimizeheat loss, the pipe is insulated with two inches (2″) of fiberglassinsulation. It will be appreciated, however, that despite theinsulation, heat is still lost from the process, i.e. from the hot waterflowing through the pipe.

Specifically, heat loss per foot of pipe, Q_(out), is equal to theoverall heat transfer coefficient from the process to the atmosphere, u,times the total heat loss surface area, A, times the difference betweenthe temperature of the water and the temperature of the atmosphere, ΔT.This is represented by the equation: Q_(out)=u*A*ΔT.

The difference between the temperature of the water and the temperatureof the atmosphere, ΔT, is one hundred and eighty degrees Fahrenheit(180° F.), i.e. 200° F. minus 20° F.

The area, A, is determinable by first taking the outside diameter of thepipe, i.e. four point five inches (4.5″), adding the thickness of theinsulation, i.e. four inches (4″) (two inches on each side), multiplyingthat calculated diameter by pi (π), and then multiplying that calculatedvalue by the length being considered, in this case, 1 foot (1 ft). Thus,the area, A, is approximately 2.224 ft².

The overall heat transfer coefficient, u, is determinable as well. Inthis case, the inverse of u equals the sum of: the inverse of theconvection coefficient of the water, h₁, which convection coefficient isapproximately 100 BTU/hour ft² ° F.; the wall thickness of the pipe, L₁,which is approximately 0.237 inches, or 0.01975 ft, divided by theconduction coefficient of the pipe, k₁, which is approximately 30BTU/hour ft ° F.; the thickness of the insulation, L₂, which isapproximately 2 inches, or 0.1667 ft, divided by the conductioncoefficient of the insulation, k₂, which is approximately 0.04 BTU/hourft ° F.; and the inverse of the convection coefficient of air, h₂, whichconvection coefficient is approximately 8 BTU/hour ft² ° F. In otherwords, l/u=l/h₁+k₁/L₁+k₂/L₂ +1/h₂. Thus, the overall heat transfercoefficient, u, is approximately 0.2324 BTU/hour ft² ° F.

The heat loss per foot of pipe, Q_(out), is approximately equal to theproduct of each of these approximations, i.e. Q_(out) is approximately93.03 BTU/hour per foot of pipe. It will be appreciated that thisapproximate value is calculated for the first foot of pipe at aninstant. Because the temperature difference, ΔT, is constantly changing,determination of heat loss for each foot thereafter becomes iterative.However, consideration of this approximation at a first foot of pipe atan instant nonetheless illustrates that insulation is commonlyinsufficient to prevent significant heat loss from a liquid or gasflowing through a pipe.

Tube Tracing Systems

Owing to this insufficiency, tube tracing systems are commonly used withpipe systems to heat, or replace heat lost from, liquids and gasesflowing through a pipe. Tube tracing systems are conventionally usedseparate from, or in combination with, insulation. FIG. 1, labeled asprior art, is a cross-sectional view of a conventional tracing systemand pipe system in which a tracer 8 is attached to a pipe 6. The tracer8 may comprise either a fluid tracer, i.e. a tube having a heatingmedium, such as steam, hot water, hot oil, or another fluid, flowingtherethrough, or an electrical tracer. Both the tracer 8 and the pipe 6are disposed within insulation 4. This type of system can becharacterized as utilizing “convection heating”, because as a practicalmatter there is essentially no conductive heat transfer path between thetracer 8 and the pipe 6. Instead, there is simply a void 5 through whichconvective heat transfer occurs.

It will be appreciated that heat transfer from the tracer 8 to the pipe6 through the void 5 is limited by the convection coefficient of thevoid 5. Commonly, the void 5 is filled with unmoving air, in which caseeven when the convection coefficient of steam flowing through the tracer8 is very high, which serves to make the convection coefficient of thevoid 5 higher over time, the heat transfer rate will still always belimited by the low convection coefficient of nonmoving air, i.e.approximately 1 to 3 BTU/hour ft² ° F. On the other hand, any attempt toincrease the convection coefficient of the void 5 by using moving aircauses a decrease in the temperature of the air.

It is useful to return to the prior example and consider the heat gainachieved utilizing the tracer 8 and void 5 of FIG. 1. Consider the same4 inch schedule 40 carbon steel pipe with the same turbulent hot waterflowing at two hundred degrees Fahrenheit (200° F.). The heat gain perfoot, Q_(in), from a tracer 8 using 50 PSIG steam as a heating source attwo hundred ninety eight degrees Fahrenheit (298° F.) can be calculatedas the product of: the surface area of heating, A, i.e. the totalsurface area exposed to the void 5, which is approximately four inches(4″), or 0.33 ft., times one foot; the difference in temperature, ΔT,between the hot water flowing through the pipe and the steam in thetracer, which is approximately one hundred degrees Fahrenheit (100° F.);and the convection coefficient of the air in the void, h₄, i.e. 1BTU/hour ft² ° F. Thus, the heat gain, Q_(in), is approximately 33BTU/hour per foot, although it will be appreciated that this calculationdoes not account for heat that the process may pull from the system.Nonetheless, it is clear even from such a rough approximation that heatgain from a tracer is at times insufficient to offset heat loss from afluid flowing through a pipe.

Other tracing systems are disclosed, for example, in U.S. Pat. No.6,595,241 to Chen, U.S. Pat. No. 4,401,156 to Wojtecki et al., U.S. Pat.No. 4,123,837 to Homer, and U.S. Pat. No. 3,331,946 to Bilbro.

In view of the foregoing, it is believe that a need exists forimprovement in heat transfer between a tracer and a pipe. This, andother needs, are addressed by one or more aspects of the presentinvention.

SUMMARY OF THE INVENTION

The present invention includes many aspects and features. Moreover,while many aspects and features relate to, and are described in, thecontext of tube tracing systems, the present invention is not limited touse only in tube tracing systems, as will become apparent from thefollowing summaries and detailed descriptions of aspects, features, andone or more embodiments of the present invention. Indeed, while theinvention is described herein with reference to heat transfer between atracing system and a pipe system, it will be appreciated that thebreadth of the invention further includes heat transfer between atracing system or similar arrangement and, for example, a tank, vessel,container, or reservoir.

Accordingly, one aspect of the present invention relates to a heattransfer element for use in tracing systems for heat transfer with apipe system. The heat transfer element includes curved mounting surfacesconfigured to mate with an outer surface of a pipe for attachmentthereto; and a channel configured to receive a tracer therein; whereinthe heat transfer element is configured to effect conductive heattransfer from the tracer to the pipe when attached with heat transfercement to both the pipe and the tracer. Preferably, the channel includesa lengthwise opening that is located along the a concave face of theheat transfer element between the curved mounting surfaces of the heattransfer element.

In a feature of this aspect of the invention, the heat transfer elementfurther includes cavities defined therein.

In a feature of this aspect of the invention, the cavities aretriangular in cross-section.

In a feature of this aspect of the invention, the heat transfer elementcomprises aluminum.

In a feature of this aspect of the invention, the heat transfer elementcomprises carbon steel.

In a feature of this aspect of the invention, the heat transfer elementcomprises stainless steel.

In a feature of this aspect of the invention, the heat transfer elementcomprises copper.

In a feature of this aspect of the invention, the heat transfer elementcomprises an aluminum alloy.

In a feature of this aspect of the invention, the heat transfer elementcomprises an aluminum alloy of grade 6061.

In a feature of this aspect of the invention, the heat transfer elementcomprises an aluminum alloy of grade 6063.

In a feature of this aspect of the invention, the heat transfer elementcomprises an aluminum alloy of grade 6005.

In a feature of this aspect of the invention, the heat transfer elementcomprises aluminum-silicon alloy A356.

In a feature of this aspect of the invention, the heat transfer elementis cast.

In a feature of this aspect of the invention, the heat transfer elementis extruded.

Another aspect of the present invention relates to a heat transfersystem. The heat transfer system includes a pipe having a fluid flowingtherethrough; a tracer configured to heat the pipe; heat transfercement; and a heat transfer element having curved mounting surfacesconfigured to mate with an outer surface of the pipe and attachedthereto via the heat transfer cement, and a channel in which the traceris received and secured via heat transfer cement; wherein the heattransfer element is configured to effect conductive heat transfer fromthe tracer to the pipe when attached with heat transfer cement to boththe pipe and the tracer.

In a feature of this aspect of the invention, the heat transfer systemfurther includes cavities defined therein.

In a feature of this aspect of the invention, the cavities aretriangular in cross-section.

Another aspect of the invention relates to a method for heat transfer.The method includes installing a heat transfer element along an extentof a pipe so as to secure a tracer to the pipe along the extent bysecuring the heat transfer element to both the pipe and the tracerutilizing heat transfer cement. The heat transfer element is configuredto effect conductive heat transfer from the tracer to the pipe throughthe heat transfer element following such securement.

Another aspect of the invention relates to a method for heat transfer.The method includes bending a tracer tube to a pipe; dry fitting a heattransfer element over the tracer tube on the pipe; removing the heattransfer element; applying heat transfer cement to the heat transferelement using an applicator; installing the heat transfer element suchthat the tracer tube is secured in close proximity to the pipe; andstrapping the heat transfer element to the pipe.

In a feature of this aspect of the invention, the method furtherincludes cutting the heat transfer element with a band saw.

Another aspect of the present invention relates to an applicator for usein applying heat transfer cement to a heat transfer element. Theapplicator includes a plurality of small protuberances dimensioned toleave small gaps between the applicator and a channel of the heattransfer element when the applicator engages the heat transfer element;and a plurality of large protuberances dimensioned to leave large gapsbetween the applicator and the heat transfer element when the applicatorengages the heat transfer element.

In a feature of this aspect of the invention, the channel is configuredto receive a tracer therein such that the tracer is retained between theheat transfer element and a pipe when the heat transfer element isattached to the pipe.

In a feature of this aspect of the invention, the channel is accessiblevia an opening between the curved mounting surfaces.

In a feature of this aspect of the invention, a top surface of the heattransfer element is located in covering relation to the tracer.

In a feature of this aspect of the invention, the tracer is permanentlysecured via heat transfer cement.

In a feature of this aspect of the invention, the tracer is retainedbetween the heat transfer element and the pipe.

Another aspect of the invention relates to a heat transfer element. Theheat transfer element includes curved mounting surfaces configured tomate with an outer surface of a pipe for attachment thereto; and achannel configured to receive a tracer therein; wherein the heattransfer element is configured to effect conductive heat transfer fromthe tracer to process flowing through the pipe when attached with heattransfer cement to both the pipe and the tracer.

In a feature of this aspect of the invention, the heat transfer elementis anodized.

In a feature of one or more aspects of the invention, the heat transferelement is configured to effect conductive heat transfer between thetracer and the pipe through the heat transfer element when the heattransfer element is attached with heat transfer cement to both the pipeand the tracer.

In a feature of one or more aspects of the invention, the heat transferelement is configured to effect conductive heat transfer between thetracer and the pipe through the curved mounting surfaces of the heattransfer element when the heat transfer element is attached with heattransfer cement to both the pipe and the tracer.

In a feature of one or more aspects of the invention, the tracercomprises an electrical tracer.

In a feature of one or more aspects of the invention, the tracerutilizes steam.

In a feature of one or more aspects of the invention, the tracerutilizes a heated fluid.

In a feature of one or more aspects of the invention, the tracerutilizes a heated liquid.

In a feature of one or more aspects of the invention, the tracerutilizes a coolant.

Other aspects relate to such a heat transfer element for use in tracingsystems for heat transfer with a tank, vessel, container, or reservoir,and systems and methods including such heat transfer element.

In addition to the aforementioned aspects and features of the presentinvention, it should be noted that the present invention furtherencompasses the various possible combinations and subcombinations ofsuch aspects and features.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more preferred embodiments of the present invention now will bedescribed in detail with reference to the accompanying drawings, whereinthe same elements are referred to with the same reference numerals, andwherein,

FIG. 1, labeled as prior art, is a cross-sectional view of aconventional tracing system and pipe system in which a tracer isattached to a pipe;

FIG. 2 illustrates an exemplary heat transfer element in accordance witha preferred embodiment of the present invention;

FIG. 3 illustrates, in a cross-sectional view, the heat transfer elementof FIG. 2 secured to the pipe of FIG. 1;

FIG. 4 illustrates conductive heat transfer utilizing the heat transferelement of FIG. 2;

FIG. 5 illustrates how a curved mounting surface can be described ascurved to mate with a circle having a certain radius;

FIG. 6 illustrates how a heat transfer element can be characterized astypically having a length (L), a width (w), a radius of curvature (r),and a channel width (A);

FIG. 7 illustrates the use of multiple heat transfer elements with asingle pipe;

FIG. 8 illustrates an elbow heat transfer element for use with anon-linear section of pipe;

FIG. 9 illustrates how a side elbow heat transfer element is configuredfor attachment to the top of an elbow pipe;

FIG. 10 illustrates how an outside, or heel, heat transfer element isconfigured for attachment to the heel of a pipe elbow;

FIG. 11 illustrates how an inside, or throat, heat transfer element isconfigured for attachment to the throat of a pipe elbow;

FIGS. 12A-B illustrate a heat transfer element configured to mate with aconcentric reducer;

FIGS. 13A-B illustrate how the heat transfer element of FIGS. 12A-B isalso suitable for use with an eccentric reducer, and further illustrateshow the heat transfer element of FIG. 2 may be suitable as well;

FIG. 14 illustrates a plurality of heel heat transfer elements spacedapart along an elbow;

FIG. 15 illustrates a heat transfer element which is similar to the heattransfer element of FIG. 1, except in that this heat transfer elementadditionally includes cavities defined therethrough in a lengthwisedirection;

FIGS. 16-19 are cross-sectional views of heat transfer elements havingdifferent cross-sectional shapes;

FIG. 20 is a cross-sectional view of a heat transfer element which haschamfered edges;

FIG. 21 is a cross-sectional view of a heat transfer element which hascorners with a 0.015 inch fillet;

FIG. 22A is a plan view of an applicator configured for use with theheat transfer element of FIG. 21;

FIG. 22B is a side plan view of the applicator of FIG. 22A;

FIG. 23 illustrates how the applicator of FIG. 22A is configured to beused with the heat transfer element of FIG. 21;

FIGS. 24A-B illustrate an applicator configured for use with the heattransfer element of FIG. 18;

FIGS. 25A-C are cross-sectional views of heat transfer elements having achannel configured to receive an electrical tracer therein; and

FIGS. 26-33 illustrate heat transfer elements configured to receivedifferent size tracers utilized together with the same pipe.

DETAILED DESCRIPTION

As a preliminary matter, it will readily be understood by one havingordinary skill in the relevant art (“Ordinary Artisan”) that the presentinvention has broad utility and application. Furthermore, any embodimentdiscussed and identified as being “preferred” is considered to be partof a best mode contemplated for carrying out the present invention.Other embodiments also may be discussed for additional illustrativepurposes in providing a full and enabling disclosure of the presentinvention. Moreover, many embodiments, such as adaptations, variations,modifications, and equivalent arrangements, will be implicitly disclosedby the embodiments described herein and fall within the scope of thepresent invention.

Accordingly, while the present invention is described herein in detailin relation to one or more embodiments, it is to be understood that thisdisclosure is illustrative and exemplary of the present invention, andis made merely for the purposes of providing a full and enablingdisclosure of the present invention. The detailed disclosure herein ofone or more embodiments is not intended, nor is to be construed, tolimit the scope of patent protection afforded the present invention,which scope is to be defined by the claims and the equivalents thereofIt is not intended that the scope of patent protection afforded thepresent invention be defined by reading into any claim a limitationfound herein that does not explicitly appear in the claim itself.

Thus, for example, any sequence(s) and/or temporal order of steps ofvarious processes or methods that are described herein are illustrativeand not restrictive. Accordingly, it should be understood that, althoughsteps of various processes or methods may be shown and described asbeing in a sequence or temporal order, the steps of any such processesor methods are not limited to being carried out in any particularsequence or order, absent an indication otherwise. Indeed, the steps insuch processes or methods generally may be carried out in variousdifferent sequences and orders while still falling within the scope ofthe present invention. Accordingly, it is intended that the scope ofpatent protection afforded the present invention is to be defined by theappended claims rather than the description set forth herein.

Additionally, it is important to note that each term used herein refersto that which the Ordinary Artisan would understand such term to meanbased on the contextual use of such term herein. To the extent that themeaning of a term used herein—as understood by the Ordinary Artisanbased on the contextual use of such term—differs in any way from anyparticular dictionary definition of such term, it is intended that themeaning of the term as understood by the Ordinary Artisan shouldprevail.

Furthermore, it is important to note that, as used herein, “a” and “an”each generally denotes “at least one,” but does not exclude a pluralityunless the contextual use dictates otherwise. Thus, reference to “apicnic basket having an apple” describes “a picnic basket having atleast one apple” as well as “a picnic basket having apples.” Incontrast, reference to “a picnic basket having a single apple” describes“a picnic basket having only one apple.”

When used herein to join a list of items, “or” denotes “at least one ofthe items,” but does not exclude a plurality of items of the list. Thus,reference to “a picnic basket having cheese or crackers” describes “apicnic basket having cheese without crackers”, “a picnic basket havingcrackers without cheese”, and “a picnic basket having both cheese andcrackers.” Finally, when used herein to join a list of items, “and”denotes “all of the items of the list.” Thus, reference to “a picnicbasket having cheese and crackers” describes “a picnic basket havingcheese, wherein the picnic basket further has crackers,” as well asdescribes “a picnic basket having crackers, wherein the picnic basketfurther has cheese.”

Referring now to the drawings, one or more preferred embodiments of thepresent invention are next described. The following description of oneor more preferred embodiments is merely exemplary in nature and is in noway intended to limit the invention, its implementations, or uses.

Turning now to the drawings, FIG. 2 illustrates an exemplary heattransfer element 10 in accordance with a preferred embodiment of thepresent invention. The heat transfer element 10 is configured for use ina conduction-assisted tracing system in accordance with one or morepreferred embodiments.

More specifically, the heat transfer element 10 is configured forattachment to a pipe as part of a tracing system. As can be seen in FIG.2, curved mounting surfaces 14 of the heat transfer element 10 areconfigured (i.e., shaped and dimensioned) to mate with a curved outersurface of a pipe. Further, a channel 16 is defined lengthwise throughthe heat transfer element 10 for receipt of a tracer. An opening of thechannel 16 is located along a concave face of the heat transfer element10 between the curved mounting surfaces 14. The tracer is receivedwithin the channel 16 through this opening when the tracer is installed,and is thereby retained against the pipe by the heat transfer element 10when the heat transfer element 10 is attached to the pipe.

FIG. 3 illustrates, in a cross-sectional view, the heat transfer element10 secured to the pipe 6 of FIG. 1. The heat transfer element 10 issecured to the pipe 6 using heat transfer cement (HTC) 12. Heat transfercement is well known, and is sometimes referred to as heat transfermastic (HTM). It will be understood that any heat transfer cement orheat transfer mastic, or any similar substance, may be utilized. It willbe appreciated that, in at least this embodiment, rather than simplybeing used to “create” surface area, the HTC 12 can be characterized as“bridging” any gap between the heat transfer element 10 and the pipe 6.Preferably, a layer of HTC 12 approximately one eighth of an inch(0.125″) thick is disposed between the heat transfer element 10 and thepipe 6.

As can be seen in FIG. 3, the heat transfer element 10 is attached tothe pipe 6 such that the tracer 8 is received in the channel 16 of theheat transfer element 10. Further, just as HTC 12 is used to bridge thegap between the heat transfer element 10 and the pipe 6, HTC 12 ispreferably used to fill the volume of the channel not filled by thetracer 8, i.e. to “bridge” any gaps between the tracer 8 and the heattransfer element 10, as well as any gap between the tracer 8 and thepipe 6. Preferably, a layer of HTC 12 approximately five one hundredthsof an inch (0.05″) thick is disposed between the heat transfer element10 and the tracer 8.

As its name implies, the heat transfer element 10 is constructed of aheat conductive material, such as, for example, aluminum, carbon steel,stainless steel, copper, an aluminum alloy, or any other heat conductivematerial. More preferably, this material comprises an aluminum alloy ofgrades 6061, 6063, or 6005, and most preferably this material comprisesaluminum-silicon alloy A356. The heat transfer element 10 is preferablyeither cast or extruded, as described in more detail hereinbelow.

The heat transfer element 10 enhances the transfer of heat from thetracer 8 to the pipe 06 by changing the nature of heat transfer fromprimarily convective heat transfer to primarily conductive heattransfer. The heat transfer element 10 can thus be characterized as“spreading out” the heat, thus effectively “creating” more surface areafor heating. Such conductive heat transfer is illustrated in FIG. 4.

In illustrating benefits of the invention, it is useful to consider heatgain achieved utilizing a tracer 8 and an exemplary heat transferelement 10 with the previous 4 inch schedule 40 carbon steel pipe havingthe same turbulent hot water flowing at two hundred degrees Fahrenheit(200° F.) therethrough. Heat gain, Q_(in), from the tracer 8 and heattransfer element 10, where the tracer 8 is once again using 50 PSIGsteam as a heating source at two hundred ninety eight degrees Fahrenheit(298° F.), can be calculated as the product of: the surface area ofheating, A, i.e. the total surface area of the heat transfer element 10which abuts the pipe 6, which is approximately two inches (2″), or0.1667 ft., times one foot; the difference in temperature, ΔT, betweenthe hot water flowing through the pipe and the steam in the tracer,which is approximately ninety eight degrees Fahrenheit (98° F.); and theoverall heat transfer coefficient from the steam to the process, u. Thisoverall heat transfer coefficient, u, is equal to the sum of: theinverse of the convection coefficient of the water, h₁, which convectioncoefficient is approximately 100 BTU/hour ft² ° F.; the wall thicknessof the pipe, L₁, which is approximately 0.237 inches, or 0.01975 ft,divided by the conduction coefficient of the pipe, k₁, which isapproximately 30 BTU/hour ft ° F.; the inverse of the overallcoefficient of the HTC 12, u_(HTC), which is approximately 35 BTU/hourft² ° F.; the estimated average path length between the tubing and theHTC 12, L₃, which is approximately one half of an inch (½″), or 0.5inches, divided by the conduction coefficient of the heat transferelement 10, which is approximately 140 BTU/hour ft ° F.; and the inverseof the convection coefficient of steam, which is approximately 500BTU/hour ft² ° F. In other words, l/u=l/h₁+L₁/k₁+l/u_(HTC)+L₃/k₃+l/h₃.The overall heat transfer coefficient, u, then, is approximately 23.98BTU/hour ft² ° F., and the heat gain, Q_(in), from the tracer 8 and heattransfer element 10 is approximately 391.68 BTU/hour per foot. Ascompared to the heat gain from a tracer 8 alone as calculatedhereinabove, this is an improvement of an order of magnitude, althoughas noted above, these calculations are approximations of beliefs.

Although described hereinabove as having a width of 2 inches (2″), heattransfer element 10 can be manufactured in various sizes and havevarying dimensions to mate with different sizes of pipes and tracers. Ina preferred implementation, a heat transfer element 10 has a width oftwo inches (2″) (plus or minus 0.1 inches) and a max length of nine feetsix inches (9′6″), although it will be appreciated that this heattransfer element can be cut into segments having shorter lengths. Itschannel 16 has a width of fifty one one hundredths of an inch (0.51″)(plus or minus 0.01 inches), thus it is dimensioned for use with a onehalf inch ( 0/5″) tracer. The distance between the top of the channel 16and the top of the heat transfer element 10 is one eighth of an inch(0.125″). Further, its curved mounting surfaces 14 can be described ascurved to mate with a circle having a particular radius, as illustratedin FIG. 5. In this preferred implementation the radius is one and threefourths inches (1.75″) (plus or minus 0.1 inches), and thus the heattransfer element 10 is sized and dimensioned for use with a three inch(3″) pipe.

It will be appreciated, then, that a particular heat transfer element 10can be partially described via several typical dimensions. Morespecifically, a heat transfer element 10 can be characterized astypically having a length (L), a width (w), a radius of curvature (r),and a channel width (A), as illustrated in FIG. 6.

In a preferred system, heat transfer elements 10 having r valuescorresponding to one inch, two inch, three inch, four inch, six inch,eight inch, and ten inch pipe are utilized. In this system, heattransfer elements 10 configured for two inch or smaller pipe have awidth, w, of one and a half inches (1.5″), while heat transfer elements10 configured for larger pipes have a width of two inches (2″). Forlarger pipes, multiple heat transfer elements 10 may be utilized, asillustrated in FIG. 7. Preferably, each heat transfer element 10 isconfigured to receive either a one half inch (0.5″) tracer or a threefourth inch (0.75″) tracer, i.e. each transfer element 10 has an A valuecorresponding to approximately one half of an inch (0.5″) or threefourths of an inch (0.75″). Alternatively, each heat transfer element 10is configured to receive a three eighths of an inch (0.375″) tracer, afive eighths of an inch (0.625″) tracer, a seven eighths of an inch(0.875″) tracer, or a one inch (1″) tracer. Although each heat transferelement 10 illustrated in FIG. 7 is configured to receive the same sizetracer, heat transfer elements 10 configured to receive different sizetracers may be utilized together with the same pipe, as illustrated inFIGS. 26-33.

Heat Transfer Elements for Non-Linear Pipe Sections

Although thus far described in the context of straight heat transferelements 10 for use with straight sections of pipe, FIG. 8 illustratesan elbow heat transfer element 30 for use with a non-linear section ofpipe. As can be seen in FIG. 8, the elbow heat transfer element 30 hasgenerally the same cross-sectional shape as a heat transfer element 10.An elbow heat transfer element can be classified by the angle of theelbow for which it is configured for attachment. Although elbow heattransfer elements are illustrated herein in the context of ninety degreeelbows, it will be understood that elbow heat transfer elements can beconfigured for attachment to an elbow of any angle. In preferredimplementations, elbow heat transfer elements configured for attachmentto forty five degree and ninety degree elbows are utilized.

An elbow heat transfer element can also be classified by where it isconfigured to attach to an elbow pipe. Elbow heat transfer element 30 isa side elbow heat transfer element because it is configured forattachment to the top or bottom of an elbow pipe, as illustrated in FIG.9. In contrast, outside, or heel, heat transfer element 40 is configuredfor attachment to the heel of a pipe elbow as illustrated in FIG. 10 andinside, or throat, heat transfer element 50 is configured for attachmentto the throat of a pipe elbow as illustrated in FIG. 11.

Similarly, FIGS. 12A-B illustrate a heat transfer element 60 configuredto mate with a concentric reducer 3. FIGS. 13A-B illustrate how heattransfer element 60 is also suitable for use with an eccentric reducer,and further illustrates how heat transfer element 10 is suitable aswell.

In at least some implementations, rather than using longer heat transferelements 10,30,40,50,60, individual heat transfer elements10,30,40,50,60 having a shorter length can be spaced apart along anexpanse of pipe. FIG. 14 illustrates a plurality of heel heat transferelements 40 spaced apart along an elbow 7.

Notably, although no insulation is illustrated in FIGS. 9-14 forclarity, insulation is preferably (and should be) used to surround eachassembly.

Alternative Cross-Sectional Shapes

Thus far, each heat transfer element 10,30,40,50,60 has been describedas having generally the same cross-sectional shape, namely thatillustrated in FIG. 3. Each heat transfer element, however, canalternatively have a different cross-sectional shape, such as, forexample, that illustrated in FIG. 15.

FIG. 15 illustrates heat transfer element 110 which is similar to heattransfer element 10 of FIG. 1, except in that heat transfer element 110additionally includes cavities 118 defined therethrough in a lengthwisedirection. It will be appreciated that the weight of the heat transferelement 110 is less than it might otherwise be if the heat transferelement 110 did not include cavities 118 due to the additional materialcosts.

Similarly, FIGS. 16 and 17 are cross-sectional views of heat transferelement 210 and heat transfer element 310, respectively. As can be seenin these figures, each heat transfer element 210,310 has a differentcross-sectional shape. Just like heat transfer element 110, thecross-sectional shape of each heat transfer element 210,310 has asmaller area comparatively to the cross-sectional shape of heat transferelement 10, and thus is comparatively lighter than a similarlydimensioned heat transfer element 10.

Other contemplated heat transfer elements have cross-sectional shapesthat differ even more markedly from that of heat transfer element 10,such as, for example, heat transfer element 410 and heat transferelement 510, illustrated in FIGS. 18 and 19 respectively. Rather thanbeing configured to retain a tracer in a channel 16 against a pipe towhich it is attached like heat transfer element 10, each of these heattransfer elements 410,510 is configured to sit between a tracer and apipe, with the pipe being secured to the mounting surfaces 414,514 andthe tracer being secured in its channel 416,516.

Some heat transfer elements have cross-sectional shapes that utilizechamfered edges. FIG. 20 is a cross-sectional view of heat transferelement 610, which includes chamfered edges 617. Any edge of any heattransfer element may utilize such chamfering. Similarly, some heattransfer elements have cross-sectional shapes that have filletedcorners. FIG. 21 is a cross-sectional view of a heat transfer element710 which has corners with a 0.015 inch fillet. Any corner of any heattransfer element may include such a fillet.

The cross-sectional shape of heat transfer element 710 corresponds topreferred dimensions for a heat transfer element. FIG. 21 includesmeasurements for these preferred dimensions.

Installation

In use, a heat transfer element can be installed on pipe with a tubetracer via the following process. First, a tube tracer is bent orpre-bent as is commonly known. Next, one or more heat transfer elementsare “dry-fitted” over the tube tracer on the pipe. The heat transferelement can be a precut to specific lengths, or, alternatively, can becut on-site using a band saw.

After being dry fit over a tube tracer, the heat transfer element isremoved, preferably with the tube tracer, although it is contemplatedthat the tube tracer may not be removed, and, in fact, may already besecured to the pipe.

HTC is next applied to the heat transfer element. Preferably, this HTCis applied using an applicator (although it could be applied manuallyusing a trowel, or otherwise). FIG. 22A is a plan view of an applicator790 configured for use with heat transfer element 710. HTC is applied tothe applicator 790 and/or the heat transfer element 710, and theapplicator 790 is then used to even the amount of HTC disposed on theheat transfer element. FIG. 23 illustrates how the applicator 790 isconfigured to be used with the heat transfer element 710. As can be seenin FIG. 23, the applicator 790 is slightly wider than the heat transferelement 710. Further, the applicator 790 is preferably one eighth of aninch (0.0125″) thick, as illustrated in FIG. 22B, which figure is a sideplan view of the applicator 790. The applicator 790 includes a pluralityof protuberances 792 shaped and dimensioned to leave gaps 794 betweenthe applicator 790 and the heat transfer element 710. The size of thesegaps 794 determines the thickness of the layer of HTC applied using theapplicator. Thus, a thicker layer of HTC is applied to the curvedmounting surfaces 714 of the heat transfer element 710 than to thechannel 716. This is preferred so that when the heat transfer element issecured to the tracer and the pipe there will be a thicker layer of HTC(preferably one eighth of an inch as noted above) between the heattransfer element 790 and the pipe, and a thinner layer of HTC(preferably five one hundredths of an inch as noted above) between theheat transfer element 710 and the tracer. Applicator 790 furtherincludes a tail 798 configured to apply HTC solely to the channel 716.

In at least some implementations, an applicator is configured to reclaimHTC from a pipe and/or tracer as well. FIG. 24A illustrates the head 496of such an applicator configured for use with heat transfer element 410.The head 496 includes a loading side 497 and a reclaiming side 498. FIG.24A illustrates how the loading side 497 can be used to apply HTC toheat transfer element 410, and FIG. 24B illustrates how the reclaimingside can be used to reclaim excess HTC 12 after installation of heattransfer element 410. Although not illustrated, the applicatorpreferably includes a handle.

After HTC is applied and the heat transfer element is secured to thepipe together with the tracer, heavy duty bands or buckles are used tostrap the heat transfer element (and tracer) in place. Preferably,stainless steel bands or buckles are used every four feet, however, itwill be appreciated that an alternative setup may be utilized.

Notably, heat transfer elements which retain the tracer betweenthemselves and the pipe have the desirable property of shielding thetracer from force applied by any strap or buckle, likely obviating therisk of compromising the integrity of the tracer.

After the heat transfer elements have been strapped on, final hook-upconnections are made. Preferably, one loop is utilized per elbow andtee. Further, it is preferable that no jumpers are used for reducers.

Manufacturing

As noted hereinabove, a heat transfer element is preferably extruded,but alternatively may be cast. Straight heat transfer elements arepreferably manufactured by making a die and extruding the shape in massproduction. Preferably, ten to twenty foot lengths are thus obtained,although in an implementation these lengths are nine feet six inches(9′6″) long. These lengths can be further cut as desired (such as, in apreferred implementation, to a max length of nine feet six inches, whichit is believed may be advantageous for transportation via, for example,shipping).

Elbow heat transfer elements (and reducer heat transfer elements andflange heaters) are preferably specially made for each size pipe elbow.Each heat transfer element is preferably extruded and then bent, but,alternatively, may be cast.

Use with Electric Tracers

Although described hereinabove largely in the context of tube tracershaving fluid flowing therethrough, a heat transfer element could equallybe utilized with an electric tracer. It will be appreciated that it iscommon to run current through an electrical wire adjacent a pipe tocreate energy, thereby heating the pipe and any product flowingtherethrough.

FIG. 25A is a cross-sectional view of a heat transfer element 810 havinga channel 816 configured to receive an electrical tracer therein. Itwill be appreciated that heat transfer elements having othercross-sectional shapes could be utilized with an electrical tracer aswell.

FIGS. 25B and 25C illustrate heat transfer elements 910 and 1010together with exemplary electrical tracers. Each exemplary tracer isillustrated as including ends of wires protruding therefrom, for ease ofunderstanding. It will be appreciated that the exemplary illustratedtracers are exactly that, exemplary, and that any type or form ofelectrical tracer may be utilized in combination with an appropriatelyconfigured heat transfer element.

Use for Cooling

Similarly, although described herein in the context of tracers utilizedfor heating, a heat transfer element could equally be utilized in acooling application, such as, for example, with a tracer having coldwater or a fluid coolant could flow therethrough for maintaining anadjacent pipe at or below a certain temperature.

Anodized Heat Transfer Elements

In a preferred embodiment, a heat transfer element is anodized.

Conclusion

Based on the foregoing description, it will be readily understood bythose persons skilled in the art that the present invention issusceptible of broad utility and application. Many embodiments andadaptations of the present invention other than those specificallydescribed herein, as well as many variations, modifications, andequivalent arrangements, will be apparent from or reasonably suggestedby the present invention and the foregoing descriptions thereof, withoutdeparting from the substance or scope of the present invention.

Accordingly, while the present invention has been described herein indetail in relation to one or more preferred embodiments, it is to beunderstood that this disclosure is only illustrative and exemplary ofthe present invention and is made merely for the purpose of providing afull and enabling disclosure of the invention. The foregoing disclosureis not intended to be construed to limit the present invention orotherwise exclude any such other embodiments, adaptations, variations,modifications or equivalent arrangements, the present invention beinglimited only by the claims appended hereto and the equivalents thereof

1-77. (canceled)
 78. A heat transfer element comprising: (a) first andsecond curved mounting surfaces configured to mate with an outer surfaceof a pipe for attachment thereto (b) first and second parallel channelwalls each extending from an interior portion of a respective one of thefirst and second curved mounting surfaces; (c) a curved channel ceilinghaving an elliptical cross-sectional shape extending between the firstand second parallel channel walls, the channel ceiling having acurvature configured to correspond to a curvature of an outer surface oftracer tubing; and (d) a lengthwise opening defined between the twocurved mounting surfaces, the lengthwise opening being an opening of aninterior lengthwise channel defined by the first and second parallelchannel walls and the curved channel ceiling, the interior lengthwisechannel being sized and dimensioned to receive tracer tubing therein;and (e) an outer surface running the length of the heat transfer elementwhich does not provide access to the interior lengthwise channel; (f)wherein the heat transfer element is configured for attachment to apipe, utilizing heat transfer cement, with tracer tubing received withinthe interior lengthwise channel such that the outer surface of the heattransfer element is located in covering relation to the interiorlengthwise channel and the tracer tubing received therein, and (g)wherein the heat transfer element comprises metal.
 79. The heat transferelement of claim 78, wherein the heat transfer element comprisesaluminum.
 80. The heat transfer element of claim 78, wherein the heattransfer element comprises extruded metal.
 81. The heat transfer elementof claim 78, wherein the heat transfer element comprises an aluminumalloy.
 82. The heat transfer element of claim 78, wherein the heattransfer element further includes one or more cavities defined therein.83. The heat transfer element of claim 82, wherein at least one of theone or more cavities has a triangular cross-sectional shape.
 84. Theheat transfer element of claim 78, wherein the heat transfer element isanodized.
 85. The heat transfer element of claim 78, wherein the heattransfer element comprises stainless steel.
 86. The heat transferelement of claim 78, wherein the heat transfer element comprises carbonsteel.
 87. The heat transfer element of claim 78, wherein the heattransfer element comprises copper.
 88. The heat transfer element ofclaim 78, wherein the heat transfer element comprises an aluminum alloy.89. The heat transfer element of claim 78, wherein the heat transferelement comprises cast metal.
 90. A method for facilitating heattransfer, comprising the steps of: (a) applying heat transfer cement toat least one of (i) a process pipe having a tracer running therealong,and (ii) a solid, heat-conductive heat transfer element comprising (A)an inner surface running a length of the heat transfer element, theinner surface comprising (1) first and second curved mounting surfacesconfigured to mate with an outer surface of a pipe for attachmentthereto, (2) first and second channel walls each extending from aninterior portion of a respective one of the first and second curvedmounting surfaces, (3) a curved channel ceiling extending between thefirst and second generally parallel channel walls, the channel ceilinghaving a curvature configured to generally correspond to a curvature ofan outer surface of tracer tubing, and (4) a lengthwise opening definedbetween the two curved mounting surfaces, the lengthwise opening beingan opening of an interior lengthwise channel defined by the first andsecond channel walls and the curved channel ceiling, the interiorlengthwise channel being sized and dimensioned to receive tracer tubingtherein, and (B) an outer surface running the length of the heattransfer element which does not provide access to the interiorlengthwise channel; and (b) installing the heat transfer element on theprocess pipe, said installing including, (i) positioning the heattransfer element over top of the process pipe and the tracer, (ii)translating the heat transfer element down over the tracer so as to (A)cause the tracer to be received within the interior lengthwise channelof the heat transfer element, the channel including heat transfer cementtherein, and (B) cause the curved mounting surfaces of the heat transferelement to abut an outer surface of the process pipe, heat transfercement being disposed on the mounting surfaces of the heat transferelement; (c) wherein the heat transfer element is installed such that,(i) the first and second curved mounting surfaces of the heat transferelement are secured to an outer surface of the process pipe, (ii) alength of the tracer is received within the interior lengthwise channelof the heat transfer element, (iii) the heat transfer element ispositioned to effect conductive heat transfer between the tracerreceived within the channel and the process pipe the heat transferelement is attached to, including conductive heat transfer through thecurved mounting surfaces of the heat transfer element, (iv) the topsurface of the heat transfer element is located in covering relation tothe interior lengthwise channel and the tracer received therein, andserves to physically protect the tracer received therein.
 91. The methodof claim 90, wherein the tracer comprises a fluid tracer.
 92. The methodof claim 90, wherein the tracer comprises an electrical tracer.
 93. Themethod of claim 90, wherein the heat transfer element is installed suchthat a continuous heat transfer cement fill layer is disposed betweenthe tracer received within the interior lengthwise channel of the heattransfer element and the process pipe the heat transfer element isattached to, the heat transfer cement fill layer comprising (a) firstand second opposed generally concave surfaces; (b) wherein the firstgenerally concave surface is in abutment with a first portion of thetracer tubing received within the interior lengthwise channel, the firstportion being disposed proximate a second portion of the pipe the heattransfer element is attached to; and (c) wherein the second generallyconcave surface is in abutment with the second portion.
 94. A heattransfer element comprising: (a) an inner surface running a length ofthe heat transfer element, the inner surface comprising (i) first andsecond curved mounting surfaces configured to mate with an outer surfaceof a pipe for attachment thereto, (ii) first and second channel wallseach extending from an interior portion of a respective one of the firstand second curved mounting surfaces, (iii) a curved channel ceilingextending between the first and second channel walls, the channelceiling having a curvature configured to correspond to a curvature of anouter surface of tracer tubing, and (iv) a lengthwise opening definedbetween the two curved mounting surfaces, the lengthwise opening beingan opening of an interior lengthwise channel defined by the first andsecond channel walls and the curved channel ceiling, the interiorlengthwise channel being sized and dimensioned to receive tracer tubingtherein; and (b) an outer surface running the length of the heattransfer element which does not provide access to the interiorlengthwise channel; (c) wherein the heat transfer element is configuredfor attachment to a pipe, utilizing heat transfer cement, with tracertubing received within the interior lengthwise channel such that (i) theheat transfer element effects conductive heat transfer between thetracer tubing received within the channel and the pipe the heat transferelement is attached to, including conductive heat transfer through thecurved mounting surfaces of the heat transfer element, (ii) the outersurface of the heat transfer element is located in covering relation tothe interior lengthwise channel and the tracer tubing received therein,and serves to physically protect the tracer tubing received therein; (d)wherein the heat transfer element is configured to allow forinstallation over installed tracer tubing by translating the heattransfer element down over installed tracer tubing secured to a tracedpipe; and (e) wherein the heat transfer element comprises metal.
 95. Theheat transfer element of claim 94, wherein the heat transfer elementcomprises aluminum.
 96. The heat transfer element of claim 94, whereinthe heat transfer element comprises extruded metal.
 97. The heattransfer element of claim 94, wherein the heat transfer elementcomprises an aluminum alloy.